DNS databases in a turbulent channel flow with passive scalar transport and a constant time-averaged heat-flux boundary condition have been used to examine the variation of the turbulent Prandtl number (Prt) across the channel. Two values of the molecular Prandtl number Pr are considered (0.025 and 0.71); in each case, data were obtained for four values of h⁺ (180, 395, 640, 1020). For Pr=0.71, Prt is 1.1 at the wall, varies between 0.9 and 1.1 in the region y⁺ <100, and is represented by 0.9 − 0.3(y/h)² for y/h >0.2. The closeness to unity near the wall is attributed to the excellent similarity between the velocity and scalar fields, whereas the decrease in magnitude in the outer region is most likely associated with the unmixedness of the scalar. A similar description for Prt is not possible for Pr=0.025 due to the strong conductive effects. In this case, the near-wall limiting value is unlikely to approach unity.